User talk:Dbz77
__TOC__ Welcome Hi, welcome to Mathematics! Thanks for your edit to the Imaginary number page. Please leave a message on my talk page if I can help with anything! -- SpikeToronto (Talk) 20:08, February 16, 2012 Zero is an imaginary number? Hi, I'd like to see your proof that zero is an imaginary number, as I was taught that a number had to have a non-zero imaginary component (as well as a zero real component) to be considered imaginary. Numbers with both components are considered complex, why don't you consider zero complex? Thanks. — Jeff G. ツ 15:41, February 17, 2012 (UTC) : Zero is complex. : Every complex number has the property of being the sum of a real and imaginary number. In order for real numbers to be complex numbers, 0 has to be an imaginary number. By including 0 in the set of imaginary numbers, every real number can be included in the set of complex numbers, since e.g. 1+0i=1, etc. : Excluding 0 from the set of imaginary numbers would mean that addition would not be closed under the imaginaries, and 0 would be the sole ''non-imaginary that couild be expressed as the sum of two imaginaries. Including 0 in the set would remove this discontinuity, and close addition under the imaginaries. : Excluding 0 from the set of imaginary numbers would yield a contradiction. The product of a real number and an imaginary number is always imaginary. If 0 was real but not imaginary, then 0*i=0 would be imaginary, a contradiction. Therefore, 0 must be imaginary. (Similarly, 0 must be real as well, since the product of two imaginary numbers is a real number, so 0*2i=0 must be a real.) :—The preceding unsigned comment was made by 96.229.217.189 (talk • • central wikia) ::That's a fascinating theory, but its extension is that all imaginary numbers are also complex because they have a zero multiplier for the real component. That is simply unacceptable, and is not supported by the references, and is thus Original Research (Wikipedia:WP:OR), which is unacceptable here. Get it published by a Verifiable Reliable Source (Wikipedia:WP:VRS) and then it will be given due weight. — Jeff G. ツ 01:25, February 21, 2012 (UTC) ::: Why is it unacceptable for the imaginary numbers to be a subset of the complex numbers? It is ''necessary for the set of complexes to include the imaginaries in order for the complexes to be an algebraic extension of the real numbers, and to be closed under addition an multiplication. For example, (3+4i)+(-3+4i) is imaginary, and (3+4i)(4+3i) is imaginary. i is a solution to the polynomial equation x^2+1=0, an equation with real coefficients. —The preceding unsigned comment was made by Dbz77 (talk • • central wikia), 04:54, February 21, 2012 (UTC) :::: Dbz77, could you please provide a verifiable reference/citation for the material you want to add to the article? Thanks! — SpikeToronto 09:26, February 21, 2012 (UTC) ::::: Here are some citations. The Imaginary Unit Pure Imaginary Course Prerequisites, Part 1 Hope this helps Dbz77 17:21, February 21, 2012 (UTC)dbz77 ::::::And those are reliable how exactly? — Jeff G. ツ 03:37, February 22, 2012 (UTC) (reset indent) Dbz77, unfortunately, those sources do not qualify as reliable sources per WP:RS, the Math Wiki’s reliable source policy. # The material at FunTrivia.com does suggest that there might be something to what you are presenting. However, there are no references/citations provided. # In contrast, the PlanetMath.org source does provide a bibliography, which could be a good starting point for you. The sources cited are as follows: #* Titu Andreescu & Dorin Andrica. Complex Numbers from A to … Z. #* Bryan E. Blank. “Book Review of An Imaginary Tale: The Story of ”, Notices of the AMS 46 10 (1999): 1236. #* Paul Nahin. An Imaginary Tale: The Story of . Princeton: Princton University Press (1998). #**See what you can find out about Paul Nahin and his book, An Imaginary Tale. That might provide a good starting place for you. # As for the JasperStreet PDF, I really am not sure. My inclination is that it would not satisfy WP:RS, but I am not 100% sure. According to the lede to the “Imaginary number” article at Wikipedia, An imaginary number is a real number multiplied by the imaginary unit , which is defined by its property .Uno Ingard, K. Fundamentals of waves & oscillations. Cambridge University Press, 1988, p.38. ISBN 0-521-33957-X The square of an imaginary number is less than or equal to zero. For example, is an imaginary number and its square is . According to some definitions, zero ( ) is not regarded as an imaginary number, but as a pure real. An imaginary number can be added to a real number to form a complex number of the form , where and are called, respectively, the real part and the imaginary part of the complex number. Imaginary numbers can therefore be thought of as complex numbers whose real part is zero. The name "imaginary number" was coined in the 17th century as a derogatory term, as such numbers were regarded by some as fictitious or useless, but today they have a variety of essential, concrete applications in science and engineering. Since the second paragraph depends upon zero being a real number, how can it also be imaginary? Anyway, you come up with a reliable source, and it can definitely go into the article, even if it ends up going into a section called something like The Zero Controversy. Thanks! — SpikeToronto 08:38, February 22, 2012 (UTC)